All Questions
24
questions
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Combinatorics Pigeon Hole Poker Game
Suppose I shuffle a standard 52 card deck deck and give you 25 cards at random from it. You are then tasked with making 5 poker hands from these cards such that each card is in exactly one hand. The ...
- 342
2
votes
4
answers
227
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Each of A, B, and C draw a card without replacement from a 52-card deck. What is the probability that A's face value is higher than the rest?
Case 1: All three cards have equal face values. There are 13 such cases since there are 13 different ranks.
Case 2: Two cards have equal face value and the third card has a lower value. Initially, I ...
- 135
2
votes
1
answer
161
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How to rank a new type of Hold 'Em Poker hand (hard)
I am trying to figure out how to rank a new type of poker hand, henceforth called a 'Block'.
A Block consists of 6 cards, and so is not possible in regular Poker - only Hold'em.
Each Block consists of ...
- 23
3
votes
1
answer
197
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Probability of having n number of cards of the same kind from drawn N cards
Introduction
Before starting, I would like to specify a few things:
The deck has 52 cards. From 1 (Ace) to 10, J, Q, K, all in four different suits: spades, diamonds, club and hearts. I don't add ...
- 110
0
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0
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49
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Which card should we change (and to what card) to maximize the probability of getting two pairs?
In a standard $52$-card deck we change 8♧ with 10♤ and 9♧ with J♤ from another deck of cards. If we change another card, which card should we change (and to what card) to maximize the probability of ...
- 33
5
votes
1
answer
224
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How is calculated the frequency of a pair, a flush of 2 cards, a straight of 2 cards and a straight flush of 2 cards (52 cards, hand of 2, 3, 4, etc)?
Introduction
Before starting, I would like to specify a few things:
The deck has 52 cards. From 1 (Ace) to 10, J, Q, K, all in four different suits: spades, diamonds, club and hearts. I don't add ...
- 110
6
votes
1
answer
631
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Why is the probability of getting a pair in a five-card poker hand so complicated?
The working-out of this question has really confused me. I know the basics of probability but I don't get the calculations here. I think 13C2 * 4C2 determines the number of possible pairs, and the ...
- 71
0
votes
2
answers
392
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Combinatorics involving a poker hand
How many 5 card poker hands can be dealt from a standard deck of 52 cards with 3 hearts and 2 diamonds?
I have tried this but I am not sure if it is correct:
${13\choose3}{13\choose2} = 22308$
- 33
2
votes
1
answer
130
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Poker - Combination Questions
I'm struggling a bit with this question so any help will be very much appreciated!
The premise is that two people, call them A and B, are playing a variant of poker where there's 3 shared cards, and ...
1
vote
1
answer
59
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Probability for hand with no sets (3+ of a kind / straight flush of 3+ cards) or potential sets (no additional card can make a set) in a card game?
Problem
In a gin variant, you win immediately if you are dealt a hand with no sets (3+ of a kind or suited run of 3+ cards) and no "potential sets", i.e. no additional card added to the hand could ...
- 453
1
vote
2
answers
166
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What's the probability for a 14-card hand to contain at least one full-house?
(This question is related to my previous question: When drawing 14 cards from a set of 52 cards, is it more likely to have a full house or two consecutive pairs?).
Problem: What is the probability ...
- 371
4
votes
1
answer
162
views
When drawing 14 cards from a set of 52 cards, is it more likely to have a full house or two consecutive pairs?
This is a problem that has been bothering me for quite some time now:
When drawing 14 cards from a set of 52 cards (standard poker deck), is it more likely to have at least one full house or at least ...
- 371
0
votes
4
answers
285
views
Combinatorics with playing cards
I have a question that I can't seem to find the answer to:
What are the odds of pulling 3 cards from a normal deck of playing cards (52 cards, 4 suits, 13 different values) and at least 2 of the ...
- 11
3
votes
1
answer
154
views
7 cards in sequence (suit does not matter)
Problem: Pick 7 cards from the regular 52 English cards deck, were they must be in order and suits don't matter (aces can loop).
As stated here for this similar problem, I suppose the answer would be ...
- 31
0
votes
1
answer
129
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Combinatorics question: Suppose you play a game of cards in which only 5 cards are dealt from a standard 52 deck.... [closed]
Suppose you play a game of cards in which only 5 cards are dealt from a standard 52 deck. How many ways are there to obtain at least 3 cards of the same suit?
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